1. Field of the Invention
The present invention relates to a peak time detecting apparatus and a peak time detecting method and, more particularly, to a peak time detecting apparatus that detects a peak time of time-series signals by using the wavelet transformation and a peak time detecting method that detects a peak time of time-series signals inputted by using the wavelet transformation.
2. Description of the Related Art
Various peak time detecting methods of the aforementioned type have been proposed, including a method in which a differential coefficient is calculated with respect to input time-series signals and, based on fluctuations of the differential coefficient, a peak and a peak time are detected, a method in which a maximum value of input time-series signals is tracked, and the maximum value retained before the signal value decreases below a pre-set threshold is set as a peak value, and the time point of detection of the maximum value is detected as a peak time, etc.
However, in the method of detecting a peak time based on fluctuations of the differential coefficient, false detection by noises is likely to occur, and the reliability is low. In the method in which when an input time-series signal drops below a pre-set threshold, the time of detection of the current maximum value is set as a peak time, detection of a peak time cannot be performed until an input signal is less than the threshold, and therefore detection of a peak time requires an amount of time.
A first peak of signals from a deceleration sensor used to activate an occupant protection apparatus that protects occupants at the time of a crash of the vehicle, such as an airbag apparatus of the like, is normally found when a bumper reinforcement provided forward of side members of a vehicle yields to an impact. Input signals up to the proximity of the first peak are used to determine a form of crash (a frontal collision, a diagonal collision, an offset collision, etc.), or to determine a timing of activating an occupant protection apparatus and a kind of the activation of the occupant protection apparatus, although the situation may vary depending on the configuration of a vehicle. If a peak time is detected with respect to signals from the deceleration sensor used by the occupant protection apparatus, the detection precision and the promptness in detecting a peak time become important factors.
It is an object of the peak time detecting apparatus and the peak time detecting method of the invention to reduce the false detections cased by noises or the like so as to detect the peak time of signals that are more precisely inputted. It is another object of the peak time detecting apparatus and the peak time detecting method of the invention to promptly detect a peak time. Furthermore, it is an object of the peak time detecting apparatus of the invention to determine the validity of peak time detection.
In order to achieve at least one of the aforementioned objects, the peak time detecting apparatus and the peak time detecting method of the invention adopt the following means.
A peak time detecting apparatus in accordance with a first aspect of the invention is a peak time detecting apparatus peak time detecting apparatus for detecting a peak time of a time-series signal by using a wavelet transformation, including: signal input means for inputting the time-series signal; product-sum operation means for performing a product-sum operation with respect to the time-series signal inputted, by using a predetermined complex function as an integral base; phase calculation means for calculating a phase based on a real number portion and an imaginary number portion of a result of the product-sum operation; and peak time determination means for determining a peak time of the time-series signal based on the phase calculated.
In the peak time detecting apparatus of the first aspect of the invention, the product-sum operation means performs the product-sum operation with respect to the time-series signal inputted by the signal input means, by using a predetermined complex function as a base of integral. The phase calculation means calculates a phase based on the real number portion and the imaginary number portion of a result of the product-sum operation. The peak time determination means determines a peak time of the time-series signal based on the calculated phase. The wavelet transformation is excellent for the analysis of a time-series signal in a time region and a frequency region, in comparison with a short-time Fourier transformation. If a transformation frequency and waveforms of the real number portion and the imaginary number portion are suitably selected, the wavelet transformation allows analysis of a targeted signal. The peak time detecting apparatus of the first aspect detects a peak time of a time-series signal through the use of a signal analysis based on the wavelet transformation.
Since the peak time detecting apparatus of the first aspect performs the product-sum operation with respect to the input time-series signal by using the predetermined complex function, and does not perform a differential operation, the peak time detecting apparatus is able to avoid false detection based on noises. As a result, the detection precision can be improved. Furthermore, since the determination of a peak time is performed based on the phase calculated based on the real number portion and the imaginary number portion of a result of the product-sum operation, the determination can be made immediately after an actual peak. Therefore, the apparatus is able to detect a peak time quickly, in comparison with an apparatus that determines a peak time when the signal becomes lower than a pre-set threshold. Furthermore, the arithmetic operations performed in the apparatus are the product-sum operation with respect to the time-series signal, the phase calculation with respect to a result of the product-sum operation, etc, and can be quickly performed. Therefore, a peak time can be promptly detected.
In the peak time detecting apparatus of the first aspect of the invention, the product-sum operation means may be means that uses a Gabor function as the predetermined complex function. Furthermore, the product-sum operation means may also be means that uses, as the predetermined complex function, a function that includes a real number portion having a localized waveform and an imaginary number portion having a localized waveform that is delayed by xcfx80/2 in phase from the real number portion. In the thus-constructed peak time detecting apparatus of the invention, the peak time determination means may be means for determining, as the peak time, a time point at which the phase calculated by the phase calculation means changes from 2xcfx80 to zero. If a function that has a real number portion having a localized waveform and an imaginary number portion having a localized waveform that is delayed by xcfx80/2 in phase from the real number portion, including the Gabor function, is used as a base of integral, the product sum of the real number portion becomes a positive value when the real number portion is superimposed on a peak of the signal. In that case, the imaginary number portion, being delayed by xcfx80/2 in phase, assumes zero, and therefore the product sum of the imaginary number portion is zero. Therefore, by suitably selecting signs of the real number portion and the imaginary number portion, it becomes possible to determine a time point at which the phase calculated based on the real number portion and the imaginary number portion of a result of the product-sum operation changes from 2xcfx80 to zero, as a time at which the signal is at a peak.
The peak time detecting apparatus of the first aspect of the invention may further include validity determination means for determining a validity of a result of determination made by the peak time determination means. Therefore, the validity of the detected peak time can be taken into account. In the thus-constructed peak time detecting apparatus of the invention,
the phase calculation means may be means for calculating a phase regarding a result of the product-sum operation with respect to a peak time detection-purposed transformation frequency and a phase regarding a result of the product-sum operation with respect to a validity determination-purposed transformation frequency that is higher than the peak time detection-purposed transformation frequency, and the validity determination means may be means for determining the validity based on the phase calculated regarding the result with respect to the validity determination-purposed transformation frequency. In the wavelet transformation, increases in the transformation frequency make it possible to detect peaks at higher frequencies in addition to a peak at a frequency intended for the signal. Therefore, the phase regarding a result of the product-sum operation using the validity determination-purposed transformation frequency that is higher than the peak time detection-purposed transformation frequency allows more sensitive peak detection than the phase regarding a result of the product-sum operation using the peak time detection-purposed transformation frequency. Therefore, by comparing the peak time detected through the use of the transformation frequency that allows more sensitive peak detection and the peak time determined by the peak time determination means, it is possible to determine the validity of the peak time determined by the peak time determination means. The determination of validity includes determination as to whether a peak time has gone without being detected, etc. In an example of such determination, if with regard to detection of a first peak time of a time-series signal, a peak is detected in the phase regarding a result of the product-sum operation using the validity determination-purposed transformation frequency whereas a corresponding peak is not detected and the time of a second peak is detected as a peak time in the phase regarding a result of the product-sum operation using the peak time detection-purposed transformation frequency, it is then determined that the determined peak time is uncertain as the first peak time in terms of validity, or is undetected. Still further, in the thus-constructed peak time detecting apparatus of the invention, the validity determination-purposed transformation frequency may be 1.0 to 2.0 times the peak time detection-purposed transformation frequency.
In the peak time detecting apparatus of the first aspect that includes the validity determination means, the validity determination means may be means for determining that a valid determination is made if a peak time is determined within a predetermined time before and after a time point at which the phase calculated regarding the result with respect to the validity determination-purposed transformation frequency changes from 2xcfx80 to zero.
Still further, in the peak time detecting apparatus of the first aspect of the invention, the time-series signal may be a signal formed by removing a high-frequency component from a signal detected by deceleration detection means provided in a vehicle, and the phase calculation means may be means for calculating a phase regarding a result of the product-sum operation with respect to a predetermined transformation frequency within a range of 100 to 150 Hz. Therefore, it becomes possible to regard the deceleration of the vehicle as a time-series signal and detect a peak time of the signal.
A peak time detecting method in accordance with a second aspect of the invention is a peak time detecting method for detecting a peak time of an input time-series signal by using a wavelet transformation, including: performing a product-sum operation with respect to the input time-series signal by using a predetermined complex function as an integral base; calculating a phase based on a real number portion and an imaginary number portion of a result of the product-sum operation; and detecting a peak time based on the phase calculated.
Since the peak time detecting method of the second aspect performs the product-sum operation with respect to the input time-series signal by using the predetermined complex function, and does not perform a differential operation, the peak time detecting method is able to avoid false detection based on noises. As a result, the detection precision can be improved. Furthermore, since the determination of a peak time is performed based on the phase calculated based on the real number portion and the imaginary number portion of a result of the product-sum operation, the determination can be made immediately after an actual peak. Therefore, the method is able to detect a peak time quickly, in comparison with a method that determines a peak time when the signal becomes lower than a pre-set threshold. Furthermore, the arithmetic operations performed in the method are the product-sum operation with respect to the time-series signal, the phase calculation with respect to a result of the product-sum operation, etc, and can be quickly performed. Therefore, a peak time can be promptly detected.
In the peak time detecting method of the second aspect of the invention, a Gabor function may be used as the predetermined complex function, or a function that includes a real number portion having a localized waveform and an imaginary number portion having a localized waveform that is delayed by xcfx80/2 in phase from the real number portion may be used as the predetermined complex function. In the thus-constructed peak time detecting method of the invention, the peak time detecting step may be a step of detecting, as the peak time, a time point at which the phase calculated changes from 2xcfx80 to zero.